Question: Solve for $x$ and $y$ by deriving an expression for $y$ from the second equation, and substituting it back into the first equation. $\begin{align*}-4x+5y &= -2 \\ -4x+6y &= -8\end{align*}$
Explanation: Begin by moving the $x$ -term in the second equation to the right side of the equation. $6y = 4x-8$ Divide both sides by $6$ to isolate $y$ $y = {\dfrac{2}{3}x - \dfrac{4}{3}}$ Substitute this expression for $y$ in the first equation. $-4x+5({\dfrac{2}{3}x - \dfrac{4}{3}}) = -2$ $-4x + \dfrac{10}{3}x - \dfrac{20}{3} = -2$ Simplify by combining terms, then solve for $x$ $-\dfrac{2}{3}x - \dfrac{20}{3} = -2$ $-\dfrac{2}{3}x = \dfrac{14}{3}$ $x = -7$ Substitute $-7$ for $x$ back into the top equation. $-4( -7)+5y = -2$ $28+5y = -2$ $5y = -30$ $y = -6$ The solution is $\enspace x = -7, \enspace y = -6$.